I've been asked to show that the system of simultaneous Diophantine equations has no solutions:
$3x+6y+z=3$
$12x+3y+2z=5$
I don't even know how to approach this problem, any help would be appreciated.
2026-03-30 21:48:26.1774907306
Prove a system of simultaneous Diophantine equations has no solution.
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Eliminate $z$: $-6x - 12y - 2z = -6$, and add this to the second equation:
$6x - 9y = -1$ or $3(2x - 3y) = -1$. This shows $3 | -1$ impossible.